Question
why do the leaves on my zucchini plant turning brown. It has a bug on it which looks like it is eating the chlorophyll.

Answer
Dear JOE,
Zucchini plants do get a type of boring parasite that kills them from the main stem.  If it's burrowed into the stem, it may have already damaged the plant to severely, but if the pest does show itself on the leaves, you should be able to kill it with the following suggestion.
I use Diatomaceous Earth as a pesticide.  It's natural and takes care of most worms and insects.  
Kind Regards,
KD Liz
www.thelandofgoshen.us